Question

identify all sets of parallel and perpendicular lines in this image.
options:
$overleftrightarrow{cd} parallel overleftrightarrow{ef}$, $overleftrightarrow{ab} perp overleftrightarrow{ef}$
$overleftrightarrow{ab} perp overleftrightarrow{cd}$, $overleftrightarrow{ab} perp overleftrightarrow{ef}$
$overleftrightarrow{cd} parallel overleftrightarrow{ef}$, $overleftrightarrow{ab} perp overleftrightarrow{cd}$
$overleftrightarrow{cd} parallel overleftrightarrow{ef}$, $overleftrightarrow{ab} perp overleftrightarrow{cd}$, $overleftrightarrow{ab} perp overleftrightarrow{ef}$

Explanation:

Step1: Identify parallel lines

Lines $\overleftrightarrow{CD}$ and $\overleftrightarrow{EF}$ are both vertical, so $\overleftrightarrow{CD} \parallel \overleftrightarrow{EF}$.

Step2: Identify perpendicular lines

The right angle symbols show $\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$ and $\overleftrightarrow{AB} \perp \overleftrightarrow{EF}$.

Step3: Combine all valid pairs

All three relationships are present: $\overleftrightarrow{CD} \parallel \overleftrightarrow{EF}$, $\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$, $\overleftrightarrow{AB} \perp \overleftrightarrow{EF}$.

Answer:

$\overleftrightarrow{CD} \parallel \overleftrightarrow{EF}$, $\overleftrightarrow{AB} \perp \overleftrightarrow{CD}$, $\overleftrightarrow{AB} \perp \overleftrightarrow{EF}$